Do you like puzzles? Many people do - they are able to relax in the face of uncertainty and play until things fall into place - whether those things are jigsaw pieces or Sudoku numbers. If you ride the GO train during rush hour, you will see some of these people, intent and relaxed, pens poised over their papers. You will also see the other kind of people, the kind who use puzzles as a test of their ability to face the problems their days will bring. They move quickly, although they may get stuck between movements; their brows are furrowed, and they look relieved, not pleased, when they finish.
Our family has gone through phases of playing with those tangled puzzles that require you free a ring or handle from a wire form (sometimes they are made with wood and/or rope). My best chance of solving those puzzles always depends on the certainty with which I approach the task: as I relax in my certainty that I'm not going to solve the puzzle, the ring slips off into my hand. This does not often happen when I settle down to analyze the shape and solve the puzzle.
It doesn't sound like strategy: I will relax and play and keep my attention elsewhere so that the solution will fall into my lap. It wouldn't help you pass grade three much less get you through grad school. Except that it might. A relaxed, resourceful mind will pick up patterns. A tense, focused mind will filter for the patterns it expects and be frustrated by the patterns that are really there. That's why Eureka! moments occur in the bathtub, under the influence of warm, flowing water.
It's hard to play with important puzzles, to sidle up to them casually and make a comment about the weather without meeting their eyes. It's hard to open ourselves to noticing what is there when we are very clear about what we want to be there. As in yoga, the greatest discipline is required for the deepest relaxation and the most consummate flexibility.